On Synthesis of Reduced Order Models

Ionutiu, R Roxana; Rommes, Joost

doi:10.1007/978-94-007-0089-5_12

Cited by 12 publications

(20 citation statements)

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“…Circuit simulators however can only handle mathematical representations to a limited extent, and reduced models have to be synthesized with RLC circuit elements. We reduce all circuits with respect to the input impedance transfer function (i.e., the inputs are the currents injected into the circuit terminals and the outputs are the voltages measured at the terminals) [123]. After converting the reduced input impedance transfer function to netlist format, the reduced circuit can be driven easily by currents or voltages when simulated.…”

Section: Circuit Representation Of Reduced Impedance Transfer Functionmentioning

confidence: 99%

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Model Order Reduction: Methods, Concepts and Properties

Antoulas

Ionutiu

Martins

et al. 2015

Mathematics in Industry

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Model order reduction : methods, concepts and propertiesAntoulas, A.C.; Ionutiu, R.; Martins, N.; ter Maten, E.J.W.; Mohaghegh, K.; Pulch, R.; Rommes, J.; Saadvandi, M.; Striebel, M.Published: 01/01/2015 Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA):Antoulas, A. C., Ionutiu, R., Martins, N., Maten, ter, E. J. W., Mohaghegh, K., Pulch, R., ... Striebel, M. (2015). Model order reduction : methods, concepts and properties. (CASA-report; Vol. 1507). Eindhoven: Technische Universiteit Eindhoven. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Here eigenvalues are the starting point. The eigenvalue problems related to large-scale dynamical systems are usually too large to be solved completely. The algorithms described in this section are efficient and effective methods for the computation of a few specific dominant eigenvalues of these large-scale systems. It is shown how these algorithms can be used for computing reduced-order models with modal approximation and Krylov-based methods. Section 3.3, written by Maryam Saadvandi and Joost Rommes, concerns passivity preserving model order reduction using the spectral zero method. It detailedly discusses two algorithms, one by Antoulas and one by Sorenson. These two approaches are based on a projection method by selecting spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros. The reduced model preserves passivity. Section 3.4, written by Roxana Ionutiu, Joost Rommes and Athanasios C. Antoulas, refines the spectra...

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Section: Circuit Representation Of Reduced Impedance Transfer Functionmentioning

confidence: 99%

“…3.4.4). Here, models obtained with dominant SZM are converted to netlist representations using the Foster impedance realization approach [118,121]. Netlist formats for the SPRIM/IOPOR [114,116,137] reduced models are obtained via the RLCSYN unstamping procedure in [123,137].…”

Section: Circuit Representation Of Reduced Impedance Transfer Functionmentioning

confidence: 99%

Model Order Reduction: Methods, Concepts and Properties

Antoulas

Ionutiu

Martins

et al. 2015

Mathematics in Industry

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“…Finally, the reduced conductance matrix can be realized as a reduced resistor network that is equivalent to the original network. This is done easily by unstampig the values in the G matrix intro the corresponding resistor values and their node connections in the netlist [68]. Since the number of resistors (and number of nodes) is smaller than in the original network, also the resulting netlist is smaller in size.…”

Section: Improved Approachmentioning

confidence: 99%

“…Here, we emphasize that applying modal approximation to reduce (5.45) directly is unsuitable especially if the underlying RC circuit has many terminals (inputs). This is because modal approximation does not preserve the structure of B and B T during reduction (for ease of understanding we denote the input-output structure loss as non-preservation of terminals) [68]. Modeling the input-output connectivity of the reduced model would require synthesis via controlled sources at the circuit terminals, and furthermore would connect all terminals with one-another [68].…”

Section: Reduction Of Rc Networkmentioning

confidence: 99%

“…This is because modal approximation does not preserve the structure of B and B T during reduction (for ease of understanding we denote the input-output structure loss as non-preservation of terminals) [68]. Modeling the input-output connectivity of the reduced model would require synthesis via controlled sources at the circuit terminals, and furthermore would connect all terminals with one-another [68]. In this chapter we present several alternatives for reducing RC netlists where not only the terminals are preserved, but also the sparsity of the reduced models.…”

Section: Reduction Of Rc Networkmentioning

confidence: 99%

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Advanced Topics in Model Order Reduction

Harutyunyan¹,

Ionutiu²,

Maten³

et al. 2015

Mathematics in Industry

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This Chapter contains three advanced topics in model order reduction (MOR): nonlinear MOR, MOR for multi-terminals (or multi-ports) and finally an application in deriving a nonlinear macromodel covering phase shift when coupling oscillators. The Sections are offered in a prefered order for reading, but can be read independentlty. terminal (or multi-port) problem. A crucial outcome of the research is that one should detect "important" internal unknowns, which one should not eliminate in order to keep a sparse reduced model. Such circuits come from verification problems, in which lots of parasitic elements are added to the original design. Analysis of effects due to parasitics is of vital importance during the design of large-scale integrated circuits, since it gives insight into how circuit performance is affected by undesired parasitic effects. Due to the increasing amount of interconnect and metal layers, parasitic extraction and simulation may become very time consuming or even unfeasible. Developments are presented, for reducing systems describing R and RC netlists resulting from parasitic extraction. The methods exploit tools from graph theory to improve sparsity preservation especially for circuits with multi-terminals. Circuit synthesis is applied after model reduction, and the resulting reduced netlists are tested with industrial circuit simulators. With the novel RC reduction method SparseMA, experiments show reduction of 95% in the number of elements and 46x speed-up in simulation time. Section 5.3, written by Davit Harutyunyan, Joost Rommes, E. Jan W. ter Maten and Wil H.A. Schilders, addresses the determination of phase shift when perturbing or coupling oscillators. It appears that for each oscillator the phase shift can be approximated by solving an additional scalar ordinary differential equation coupled to the main system of equations. This introduces a nonlinear coupling effect to the phase shift. That just one scalar evolution equation can describe this is a great outcome of Model Order Reduction. The motivation behind this example is described as follows. Design of integrated RF circuits requires detailed insight in the behavior of the used components. Unintended coupling and perturbation effects need to be accounted for before production, but full simulation of these effects can be expensive or infeasible. In this Section we present a method to build nonlinear phase macromodels of voltage controlled oscillators. These models can be used to accurately predict the behavior of individual and mutually coupled oscillators under perturbation at a lower cost than full circuit simulations. The approach is illustrated by numerical experiments with realistic designs. Model Order Reduction of Nonlinear Network Problems1 The dynamics of an electrical circuit can in general be described by a nonlinear, first order, differential-algebraic equation (DAE) system of the form:q(x(t)) + j(x(t)) + Bu(t) = 0, (5.1a)completed with the output mapping 1 Section 5.1 has been written by Michael Striebel and E. ...

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Model order reduction of nonlinear circuit equations

Steinbrecher

Stykel

2012

Circuit Theory & Apps

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SUMMARY In this paper, we present a model order reduction approach for nonlinear circuit equations with a small number of nonlinear elements. This approach is based on the decoupling of linear and nonlinear subcircuits and reducing the linear part using balancing‐related model reduction techniques. The efficiency and applicability of the proposed model reduction approach is demonstrated on numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.

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On Synthesis of Reduced Order Models

Cited by 12 publications

References 17 publications

Model Order Reduction: Methods, Concepts and Properties

Model Order Reduction: Methods, Concepts and Properties

Advanced Topics in Model Order Reduction

Model order reduction of nonlinear circuit equations

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